strategy gas transm

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Energy Policy 35 (2007) 56565670

A strategic planning model for natural gas transmission networks

Alireza Kabiriana,, Mohammad Reza Hemmatib

aDepartment of Industrial and Manufacturing Systems Engineering, Iowa State University, 2019 Black Engineering, Ames, IA 50011, USAbDepartment of Chemical Engineering, Sharif University of Technology, Tehran, Iran

Received 3 March 2007; accepted 18 May 2007

Available online 1 August 2007

Abstract

The design and development of natural gas transmission pipeline networks are multidisciplinary problems that require variousengineering knowledge. In this problem, the type, location, and installation schedule of major physical components of a network

including pipelines and compressor stations are decided upon over a planning horizon with least cost goal and subject to network

constraints. Practically, this problem has been viewed as a conceptual design case and not as an optimization problem that tries to select

the best design option among a set of possible solutions. Consequently, conceptual design approaches are usually suboptimal and work

only for short-run development planning. We propose an integrated nonlinear optimization model for this problem. This model provides

the best development plans for an existing network over a long-run planning horizon with least discounted operating and capital costs. A

heuristic random search optimization method is also developed to solve the model. We show the application of the model through a

simple case study and discuss how non-economic objectives may also be incorporated into model.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Natural gas pipeline network; Strategic planning; Nonlinear optimization

1. Introduction

Development and planning of natural gas transmission

networks as multidisciplinary projects have crucial impact

on the economy of gas-rich countries like Iran. The

investment costs and operation expenses of pipeline

networks are so large that even small improvements in

system utilization and planning can involve substantial

amounts of money.

The natural gas industry services include producing,

moving, and selling gas. Our main interest in this study is

focused on the transportation of gas through a pipelinenetwork. Moving gas is divided into two classes: transmis-

sion and distribution. Transmission of gas means moving a

large volume of gas at high pressures over long distances

from a gas source to distribution centers. In contrast, gas

distribution is the process of routing gas to individual

customers. For both transmission and distribution net-

works, the gas flows through various devices including

pipes, regulators, valves, and compressors. We further

narrow down our focus in this study to transmission

networks. The problem addressed in this paper involves

decisions upon the development plans of an existing

natural gas transmission network for a study area in a

long-run horizon in order to satisfy the demand of some

consumers.

Over the years, various aspects of the problem have been

addressed (Larson and Wong, 1968; Graham et al., 1971;

Martch and McCall, 1972; Flanigan, 1972; Mah and

Schacham, 1978; Cheesman, 1971a, b; Edgar et al., 1978).

Larson and Wong (1968) determined the steady-stateoptimal operating conditions of a straight natural pipeline

with compressors in series using dynamic programming to

find the optimal suction and discharge pressures. The

length and diameter of the pipeline segment were assumed

to be constant because of limitations of dynamic program-

ming.Martch and McCall (1972)modified the problem by

adding branches to the pipeline segments. However, the

transmission network was predetermined because of the

limitations of the optimization technique used. Cheesman

(1971)introduced a computer optimizing code in addition

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Corresponding author. Tel.: +1 515294 1682; fax: +1 515294 3524.

E-mail address: [email protected] (A. Kabirian).
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to Martch and McCall (1972) problem. They considered

the length and diameters of the pipeline segments to be

variables. But their problem formulation did not allow

unbranched network, so complicated network systems

could not be handled.Olorunniwo (1981)andOlorunniwo

and Jensen (1982) provided further breakthrough by

optimizing a gas transmission network including the typeand location of pipelines and compressor stations. Edgar

and Himmelblau (1988) simplified the problem addressed

byOlorunniwo (1981)andOlorunniwo and Jensen (1982)

to make sure that the various factors involved in the design

are clear. They assumed the gas quantity to be transferred

along with the suction and discharge pressures to be given

in the problem statement. They optimized the variables

such as the number of compressor stations, the length of

pipeline segments between the compressors stations, the

diameters of the pipeline segments and the suction, and

discharge pressures at each station. They considered the

minimization of the total cost of operation per year

including the capital cost in their objective function against

which the above parameters are to be optimized. Edgar and

Himmelblau (1988)also considered two possible scenarios:

(1) the capital cost of the compressor stations is linear

function of the horse power and (2) the capital cost of the

compressor stations is linear function of the horsepower

with a fixed capital outlay for zero horsepower.

The development planning of natural gas network

requires various engineering, economics, and management

knowledge. But what practically is done in developing

countries like Iran, which holds the second largest natural

gas resources in the world, is based on conceptual designs

of engineers to satisfy short-run demand of consumers.Pursuing this policy over years has led to a complex and

inefficient pipeline network that is growing annually. On

the other hand in theory, the literature also lacks an

integrated strategic planning method to consider different

aspects of the problem over a long-run horizon. Specifi-

cally, these issues include:

1. The short-run development planning in the heart of a

long-run strategic plan,

2. The best type and location of the new compressor

stations,

3. The best type and routing of the pipelines,

4. The scheduling of implementing new pipelines and

compressor stations in the network,

5. The best combination of natural gas procurement from

available sources, and

6. The best operating conditions of compressor stations in

different periods of each year of the long-run horizon.

In this paper, we provide an optimization model to

address these issues. This strategic planning model is a

complement to the available studies in the literature and

could bridge the gap between the theoretical researches and

practical needs. In addition to the model, a specific

heuristic random search algorithm is also developed which

could solve the proposed strategic planning model and

provide (near) optimal development plans over the long-

run planning horizon.

The remainder of this paper is organized as follows.

Section 2 discusses about the model. After introducing the

notation and main parameters of the model in Sections 2.2

and 2.3, we talk about the integrated model of this paperby introducing decision variables, constraints, and objec-

tive function. There is a submodel within the integrated

model that finds best operating condition of the network

over time. This submodel is discussed in Section 2.5. The

optimization algorithm of the model is discussed in Section

3 and we use a case study in Section 4 to demonstrate the

applicability of the model and the proposed solver method.

Section 5 discusses about the flexibility of the model in

incorporating various decision criteria and constraints in

the planning model. Finally, Section 6 concludes the paper.

2. Proposed model

We discuss about the model of this paper in this section.

Before going through the details, we briefly introduce all

notations inTable 1.

2.1. Problem definition

The problem addressed in this paper focuses on

transmission of high-pressure processed natural gas from

production facilities to distribution centers or major

consumption sites. The development and extension projects

of a natural gas transmission network have differentphases, which differ from country to country based on

the rules and economic policies imposed by the govern-

ments. The major phases of a typical development project

in the US are provided in Table 2 (Transportation

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Table 1

Parameters of the model

Notation Parameter, sets, and variables

o Length of long-run planning horizon

u Length of short-run planning horizon

l Number of short horizons in a long horizon

Cjk Set of supply nodes inkth year ofjth short horizonDjk Set of demand nodes inkth year ofjth short horizon

ijk Lower bound of gas supply ofith node inkth year ofjthshort horizon

dijk Upper bound of gas supply ofith node in kth year ofjth

short horizon

t The number of periods of a year

yijkl The demand ofith node inlth period ofkth year ofjth short

horizon

Zijkl Upper bound of the pressure demanded/supplied inith node

at lth period ofkth year ofjth short horizon

gijkl Lower bound of the pressure demanded/supplied inith node

at lth period ofkth year ofjth short horizon

Ij Available compressor station entrance nodes at short

horizonj

Oj Available compressor station exit nodes at short horizonj

A. Kabirian, M.R. Hemmati / Energy Policy 35 (2007) 56565670 5657


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Research Board of the National Academies, 2004). The

procedures for other countries, though officially different,

have similarities to the major steps described in the table.

We will focus our attention in this paper on the first phase

inTable 2.

We assume that there exists a study area with an existing

natural gas pipeline network. There is also a long-run

planning horizon for this study area. The study area has a

number of consumption centers/sources of gas supply with

known demand/supply range over the long-run horizon.

The problem addressed here is finding the best feasibledevelopment plans for the gas transmission network over

the long-run horizon based on the existing network. Best

here means least discounted operating and capital costs

paid over the long horizon and by feasible we mean

satisfying all structural, technical, and planning con-

straints.

2.2. Planning horizons

The model assumes a long-run planning horizon

consisting of a number short-run planning horizons with

equal length. We assume that the lengths of long and shorthorizons are o and u years respectively, and the long

horizon has l short horizons. Simply, we have

o lu.

The key assumption here is that the structure of the

network at the end of short horizon j must be capable of

satisfying the total demand of all consumers during all

years of short horizon j 1. Hence, the available useable

structure of the network for a short horizon is fixed during

all years of the short horizon. But the structure of the

network could be changed during short horizons; these

changes are either in the combination of pipelines or in

compressor stations.

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Table 1 (continued)

Notation Parameter, sets, and variables

Hj The union of sets Ijand OjTj The set of potential transshipment nodes for short horizonj

Aj The set of active transshipment nodes for short horizonj

r Number of different types of pipe

s Number of different types of compressor stationsGii0j Set of pipe types between nodesiandi

0 in the available

network of short horizon j

mii0j Compressor station type between nodesiandi0 in available


Pj Set of pipe edges in the available network of short horizonj

Kj Set of compressor station edges in the available network of

short horizonj

Xii0jm Type code ofnth new pipe between nodes iandi0 in

development plan for jth short horizon

x Maximum number of new pipes between two nodes in a

development plan

w Discount rate

NPW Objective function of the model (net present worth)

ajk Capital cost paid at kth year ofjth short horizon

bjk Optimum operating cost paid at kth year ofjth short

horizon

acaa0j Capital cost of replacing compressor station typea with

compressor station type a 0 at jth short horizon

ap

bii0j Capital cost of installing pipeline typebbetween nodesiand

l0 at jth short horizon

nck Percent of the capital cost of compressor stations in a

development plan for each short horizon which occurs inkth

year

npk

Percent of the capital cost of pipelines in a development plan

for each short horizon which occurs in kth year

Bjk Financial budget available for kth year ofjth short horizon

Wijkl The pressure in ith node at lth period ofkth year ofjth

planning horizon

Vhii

0

jkl The mass flow rate inhth pipe between nodes iand l0 atlth

period ofkth year ofjth short horizon

Wii0j Number of pipelines between nodesi,l0 in the available


tl The time point in each year whenlth period ends

bjk Operating cost paid at kth year ofjth short horizon

$jkl Operating cost paid at lth period ofkth year ofjth short

horizon

$

jkl Optimum operating cost paid atlth period ofkth year ofjth

short horizon

$c

jkl Operating cost of compressor stations atlth period ofkth

year ofjth short horizon

$s

jkl Operating cost of gas supply atlth period ofkth year ofjth

short horizon

psijklM; P The price function of one mass unit natural gas inith supply

node at lth period ofkth year ofjth short horizon ifrequested mass flow rate out of the node and pressure are M

andP, respectively

pcjkl The price of one mass unit natural gas consumed in a

compressor station at lth period ofkth year ofjth short

horizon

pfjkT

Annual fixed operating cost function of a compressor

station of type Tat kth year ofjth short horizon

kM; I; O; T Mass flow rate function consumed by a compressor stationof type Twhere the incoming mass flow rate ofMwith

pressure I is delivered with an outgoing pressure ofO.

z Pipe resistance which is a function of type and length of pipe

O(T) The set of feasible vectors of (incoming mass flow rate (M),

inlet pressure (I), outlet pressure(O)) for a compressor

station of type T

Table 2

Phases of a typical natural gas development project in the Unites States

Phase Description

1. Feasibility study Working on economic studies and construction

plans

Analyzing environmental impacts of the pipeline s

construction and operation

2. Certificates from

FERC

Submitting feasibility study reports to Federal

Energy Regularity Commission (FERC)

Obtaining certificate of public convenience and

necessity

3. Right of way Purchasing the right of way and leasing the surface

property along the path of the proposed

construction

4. Ordering

equipments

Ordering the pipes, and fittings and delivering them

5. Installation and

utilization

Installing physical components of the network

Inspection

Utililization

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The model plans some changes in the network structure

for each short horizon. These changes could be considered

as development plans. We assume that the development

plan for short horizon j 1 are implemented during

previous short horizons and finished no later than the

end of short horizon j. So the changes in the structure are

available to be utilized in short horizonj1. The planned-ahead changes for the first short horizon are implemented

before the start of the long horizon. The model considers a

short horizon called short horizon zero before the first

short horizon, so that the required changes for the first

short horizon are implemented until the end of the short

horizon zero. The hidden assumption here is that the

demand of all consumers before the start of the long

horizon is met by the available network before long

horizon.

2.3. Network structure

The model assumes a study area that has some natural

gas consumers and suppliers during long horizon.

The major physical components of a real gas transmis-

sion network are pipelines and compressor stations. These

two components are represented by some edges in the

network of the model; one edge for each pipe and one edge

for each compressor station.

Along with the mentioned edges, the network has five

types of nodes:

Demand nodes.

Supply nodes. Compressor station entrance nodes. Compressor station exit nodes. Transshipment nodes.

The demand nodes are major locations of consuming

natural gas in the study area. The demand nodes are either

the central point of major consumption regions in the study

area or export terminals of natural gas from the study area

to outside. In contrast, supply nodes are locations of

resources of processed natural gas in the study area. These

nodes are either refineries or plants producing natural gas

or the import terminals of natural gas from outside of the

study area.

Entrance nodes of compressor stations are points where

gas enters a compressor station edge to be compressed.

Another set of nodes, exit nodes, are considered at the end

of compressor station edges, where compressed gas flows

through the network by compressor stations.

Transshipment nodes are the places where more than 2

pipe edges are joined. In each transshipment node, the gas

flows into the node via some pipe(s) and flows out through

some other(s).

Each node in the network is assigned a unique code in

the model. The edges are recognized by the codes of their

corresponding end nodes.

2.3.1. Demand and supply parameters

The combination of locations of demand and

supply nodes must be forecasted by the modeler.

We assume that these combinations are fixed during

each year of long horizon, but can be modified at the

end of each year; for instance, a new gas supplier may

be added at the end of year j to the combination ofsupply nodes for this year so that the new supplier may

start to feed gas into network from the beginning of year

j1. We denote the sets of supply and demand nodes in

kth year of jth short horizon by Cjk and Djk, respectively,

where

j 1; 2;. . .;l; k 1; 2;. . .; u.

We also need to define the sets of supply and demand

nodes for the last year of planning horizon zero; these two

sets are denoted by C0;u and D0;u, respectively.

In this paper, the demand and supply are measured by

their mass flow rate (kg/year). We assume that the amount

of potential gas supply in each supply node is limited to arange. These ranges must be forecasted in order to

construct and run the model. The parameters ijk and dijkrepresent upper and lower bounds of gas supply ofith node

inkth year ofjth short horizon where

i2 Cjk; j 1; 2;. . .;l; k 1; 2;. . .; u.

The model also requires the forecasts of the demand for

each demand node over the long horizon. The actual

demands follow specific time series and are continuous

functions of time. But for simplicity, each year is split into

a number of periods, say t periods, and the model tries to

satisfy the forecasted average demand of each period. Thelth period of each year starts at time tl1 and ends at tl,

where we set t0 0 and tt 1. We denote the forecasted

average demand ofith node in lth period ofkth year ofjth

short horizon by y ijkl, where

i2 Djk; j 1; 2;. . .;l; j 1; 2;. . .;l; l1; 2;. . .; t.

The demand nodes not only consume a specific mass

flow rate in each period, but also need the pressure of the

gas to be within a range. Also, the supply nodes release the

gas with a pressure that is bounded to a range. We denote

the user-defined upper and lower bounds of the pressure

demanded/supplied inith node at lth period ofkth year ofjth short horizon by Zijkland gijkl, respectively, where

i2 Djk[ Cjk; j 1; 2;. . .;l; k 1; 2;. . .; u;

l1; 2;. . .; t.

2.3.2. Parameters of network components

The sets of available compressor station entrance and

exit nodes at short horizon j are denoted by Ij and Oj,

respectively. We also define the set Hj as the union of IjandOj where

j 0; 1;. . .;l.

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Transshipment nodes as the potential locations of joint

of a number of pipes help the model find optimal pipeline

routes with the goal of least total net present cost. The

modeler selects a set of points inside the study area for each

short horizon where by the new pipes in the development

plans may join at these points. But these potential points

are not necessarily the joint place of pipes because theoptimal routes obtained by the model may pass through

specific transshipment nodes and ignore the others due to

cost issues. A transshipment node is called active if it is

the joint location of pipes; otherwise, it is named

inactive. We denote the set of potential transshipment

nodes for short horizonjwithTjwhich is a combination of

active and inactive transshipment nodes. The set of active

transshipment nodes in the available pipeline network at

jth short horizon is also denoted by Aj where

j 0; 1;. . .;l.

Two types of edges were defined for the network of the

model. We suppose that the number of different pipe edges

is limited. Specifically, there arerdifferent types of pipeline

that could be used in the network. These pipes which have

unique type codes may differ in technical specifications

such as diameter, thickness, etc. Similarly, we suppose that

there are s different types of compressor stations. Again,

these compressor stations may differ in technical specifica-

tions like the number of compressors, fuel, etc. and have

unique type codes.

The set of pipe edges in the available network of short

horizon j is denoted by Pj. The members of this set are

vectors (i,i0) where ioi0 and i,i0 are 2 adjacent nodes

through a pipe. If more than 1 pipe link i,i0 (parallel pipeedges in the network), the set of pipe edges includes vector

(i,i0) as many as the number of parallel pipes between the

corresponding nodes. Similarly, we define Kjas the set of

compressor station edges containing vectors (i,i0) where

ioi0 and i,i0 are 2 adjacent nodes through a compressor

station. Again we have

j 0; 1;. . .;l.

We also defineGii0jas the set of pipe types betweeni, and

i0 in available network of short horizon j. Clearly, if only

one pipe links i,i0 for short horizon j, Gii0j has just one

member which is the type code of the pipe. We have

i; i0 2Pj; j 0; 1;. . .;l.

Similarly, the compressor station type between i; andi0

in available network of short horizon j is denoted by mii0jwhere

i; i0 2Kj; j 0; 1;. . .;l.

2.4. Integrated model

The integrated strategic planning model is an optimiza-

tion framework, which involves an objective function and a

number of constraints. This optimization model is math-

ematically presented in this section after defining decision

variables of the planning problem.

2.4.1. Decision variables

Development plans are nothing but the type and location

of new pipes and compressor stations in the network. So we

define one set of decision variables for pipes and anotherset for compressor stations.

Any two nodes that are not adjacent with a compressor

station edge may be planned to be linked with one or more

pipes in a development plan for a short horizon. Let us

denote the type code ofnth new pipe between nodes i; i0 indevelopment plan for jth short horizon by Xii0jn (note that

more than 1 pipe may be installed between 2 points) where

ioi0; i; i0 2Cj;u[Dj;u[Tj[ Hj1

i; i0eKj1; j 1; 2;. . .;l; n 1; 2;. . .;x,

wherex is the maximum number of new pipes between any

2 nodes in a development plan; this user-defined parameterlimits the set of pipe decision variable. If no pipe is planned

between 2 nodes in a development plan, the corresponding

decision variable takes zero. We have

Xii0jn2 f0; 1; 2;. . .;rg.

We assume that the new compressor stations are located

in the middle of some pipe edges. This means that the

optimization algorithm of the model selects some pipe

edges and split each in to 3 edges; 2 pipe edges and one

compressor station edge between them. In order to define

the new decision variable, we need to define the updated

pipe set Pj1 as

Pj1Pj1[ fi; i0ioi0; i; i0 2Cj;u[Dj;u[Tj[ Hj1;

i; i0eKj1; Xxn1

Xii0jna0g 1

The setPj1contains the pipe edges in available network

of short horizonj1 and new pipes that are planned in the

development plan of short horizon j.

We define decision variable Yii0j as the compressor

station type that is planned to be installed in the middle of

pipe edgei; i0in the development plan ofjth short horizonwhere

ioi0; i; i0 2Pj1; j 1; 2;. . .;l.

Another possibility for compressor station decision

variable is the case that a previously installed compressor

station is upgraded in a development plan. Therefore, we

extend the definition of the decision variable Yii0j to the

type code of upgraded compressor station that replaces

with existent compressor station i; i0 in the developmentplan ofjth short horizon where

ioi0; i; i0 2Kj1; j 1; 2;. . .;l.

Like decision variable Xii0jn, we set Yii0j0 if no new

compressor station is planned to be installed between

nodes i and i0 in development plan of jth short horizon.

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Any way, we have

Yii0j2 f0; 1; 2;. . .;sg.

2.4.2. Objective function

Various goals may be pursued in gas transmission

pipelines network design and planning. Among these, cost,reliability, and responsiveness are probably the most

important and evident. But in addition to these objectives,

environmental and social criteria must also be considered

in the planning model to ensure a sustainable development.

Our objective function here nominally includes cost-related

objectives. Specifically, we use the net present worth

(NPW) of operating and capital costs in long-run horizons.

In Section 5, we discuss how various other objectives may

be incorporated into the cost-based objective function of

the model.

Considering a cash flow of costs and possibly revenues

related to installation and operation of the network, wecalculate the NPW at the beginning of long horizon as the

objective function to be minimized:

min NPWXlj0

Xnk1

ajk b

jk

1wj1uk1,

wherew is the effective annual interest rate and ajkandb

jk

are, respectively, capital and optimal operating costs atkth

year of jth short horizon, so that

j 0; 1; :::; l1; k 1; 2; :::; u,

We assume that the capital and operation costs are

occurred at the beginning of the year.

The capital costs occurred in each short horizon are

functions of the variables of development plan for the

subsequent short horizon (remember that the development

plan for a short horizon is implemented in its previous

short horizon). Specifically, the two decision variables sets

defined earlier, pipeline and compressor station variables,

are the only variables that affect the capital cost function.

In contrast, this is not the case for operating costs because

there are 2 other sets of variables along with pipeline and

compressor station variables that could alter the values of

operating cost. These new variables as the decisionvariables of the so-called Submodel are pressure of the

gas in nodes and the mass flow rate in pipes. Given a

network structure for satisfying the demand of consumers

for a period, different combinations of pressure and mass

flow rate may be found that could be technically feasible;

hence, we define bjk as the total minimum (optimum)

operating cost of all periods ofkth year ofjth short horizon

if the combination of pressure and mass flow rate variables

for all periods of the corresponding year take their optimal

values that lead to least operating costs.

We also set

al;k0; b0;k0; k 1; 2;. . .; u.

2.4.2.1. Capital costs. We assume that the capital cost of

installing a compressor station varies for different short

horizons and is a function of the compressor station type.

Let us denote this capital cost of replacing compressor

station typea with compressor station type a0 at jth short

horizon withacaa0j. Ifa0 0, no compressor station already

exists in the installation location to be upgraded and acaa0j is

just the capital cost of a new compressor station type a at

jth short horizon. We assume that the capital cost of a

pipeline is a function of pipe type and locations of end

nodes; this cost varies for different short horizons as well.

Let us denote the capital cost of installing pipeline type b

between nodes iand i0 at jth short horizon with ap

bii0j. For

these parameters,

a 1; 2;. . .;s; a0 0; 1;. . .;s; a a0;

b 1; 2;. . .;r; j 0; 1;. . .;l1.

Now we calculate the total capital cost ajk as

ajkX

i;i0 i;i02Kj1Kj nck acmi;i0 ;j1;0;j

X

i;i0 i;i02Kj1\Kj; mi;i0 ;j1ami;i0 ;j

nck a

cmi;i0 ;j1;mi;i0 ;j;j

X

i;i0 i;i02Pj

Pj

n oXzm1

npk a

p

Xi;i0 ;j1;m;i;i0j

j 0; 1;. . .;l1; k 1; 2;. . .; u,

wherenckandnpkare, respectively, the percent of capital cost of

installing compressor stations and pipelines for each short

horizon which occur in kth year. Of course, we must have

Xuk1

nck1;Xuk1

npk1.

2.4.2.2. Operating costs. Generally, operating cost for the

pipeline network are those costs that are not classified as

capital costs. We only consider two major operating costs

in the model:

The operating cost of compressor stations. The supply cost of natural gas to the network.

Compressor stations as the hearts of the network

consume energy to increase gas pressure in the network.

These stations have some other operating costs such as

maintenance, labor, and overhead.

The gas is supplied to the network by different sources

including refineries and importation from outside of the study

area. Given the forecast of the consumption in demand nodes

for a period, one may find different combination of gas

supply from supply nodes to satisfy the demands. But, the

sales cost of gas from the supply nodes to the network could

be different for different supply nodes. So the combination of

gas supply could affect the costs of model. Therefore, we also

define the operating cost of gas supply.

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Given a fixed network structure for a period, both

operating cost defined above are functions of steady-state

mass flow rate in the pipes and gas pressure in the nodes. In

fact, whenever we have a fixed structure for the network to

satisfy the demand of some consumers, we may find

different combination of mass flow rate and pressure

variables for different parts of the network that can satisfydemands. These different combinations of mass flow rates

and pressures could have different operating costs. Hence,

there must be an optimization model within our integrated

model to find the best combination of mass flow rates and

pressures in the network for a given network structure. We

call this new optimization model as submodel. The

objective function of this submodel is minimization of the

operating cost. This submodel is subject to many technical

constraints.

The procedure that is used in our model is that whenever

we have a fixed network structure for a period, we run the

submodel to find least possible operating cost for the given

network, then this cost is plugged into the objective

function of our integrated model.

As we will see in Section 2.4.3, some constraints of the

integrated model are also affected by the best feasible

values of mass flow rates and pressure variables of the

network. So, we postpone discussing about more details of

the submodel problem until Section 2.5.

2.4.3. Constraints

There are 4 classes of constraints for the integrated

model as follows (in Section 5, we discuss how various

other constraints including some environmental and social

limitations may be incorporated into model):

Class1: domain of variables.

Class 2: network structure constraints.

Class 3: financial budget constraints.

Class 4: submodel constraints.

We informally provided the first-class constraints when

we defined the decision variables of integrated model. The

first set of decision variables Xii0jn could only take these

values:

Xii0

jn2 f0; 1; 2; :::; rg,

ioi0; i; i0 2Cj;u[Dj;u[Tj[ Hj1;

i; i0eKj1; j 1; 2;. . .;l; n 1; 2;. . .;x.

Similarly, for the second set of decision variables Yii0j,

Yii0j2 f0; 1; 2;. . .;sg,

ioi0; i; i0 2Pj1; j 1; 2;. . .;l.

The second class of constraints refers to the feasible

structures of the network. Applying these constraints, the

model searches best structures of the network among

logically acceptable options. Three types of this class of

constraints are as follows:

1. There must be at least one path between any demand

node (with a positive demand) and at least one of the

supply nodes; otherwise there is no way that the given

network structure could satisfy the consumption of thedemand nodes. Many algorithms exist in graph theory

to check the existence of these paths (see Ore, 1963;

Harary, 1969).

2. The structure of the network must not have transship-

ment nodes that are adjacent to exactly one edge. In

other words, the number of pipes or compressor stations

connected by a transshipment node must be zero or

more than 2.

3. The transshipment nodes cannot be the joints place of

any combination of pipes. Technically, it may be

infeasible to join specific types of pipes together. These

constraints must be defined with more details based onthe type of available pipelines and engineering designs.

In the 3rd class of constraints, the total financial budget

available in each year of the long horizon is assumed to be

limited. If this budget for the kth year ofjth short horizon

is denoted by Bjk,

ajk b

jkpBjk,

j 0; 1; 2;. . .;l; k 1; 2;. . .; u.

The 4th class of constraints is basically the constraints of

the submodel introduced in Section 2.4.2.2. In the perspective

of integrated model, these constraints are generally defined tomake sure that the network structures under study can meet

the demand of consumers. We discuss about the details of

submodel constraints in Section 2.5.3.

2.5. Control optimization submodel

In Section 2.4, we discussed about the necessity of having

a submodel in the heart of the integrated model to find the

least possible operating cost and check some of the

constraints of integrated model. The submodel which is

called steady-state simulation of pipeline network in the

literature is essentially the optimization model of mass flow

rates and pressure in the network subject to some technical

constraints and with operating costs as objective function.

The submodel problem differs from traditional network

flow problems in some fundamental aspects (Ros Mercado

et al., 2006). First, in addition to the flow variables for each

edge, which in this case represent mass flow rates, a pressure

variable is defined at every node. Second, besides the mass

balance constraints, there exist two other types of major

constraints: (i) a nonlinear equality constraint on each pipe,

which represents the relationship between the pressure drop

and the flow and (ii) a nonlinear nonconvex set, which

represents the feasible operating limits for pressure and flow

within each compressor station. The objective function is

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given by a nonlinear function of flow rates and pressures. In

the real world, these types of instances are very large both in

terms of the number of decision variables and the number of

constraints, and very complex due to the presence of

nonlinearity and nonconvexity in both the set of feasible

solutions and the objective function.

The submodel must be run for each period of each yearof any given network structure of a short horizon. So, we

develop the submodel concepts for an arbitrary period, say

lth period ofkth year of jth short horizon.

2.5.1. Decision variables of submodel

The submodel has 2 sets of decision variables. The first

set is the gas pressure in all nodes of the network. Let us

denote the pressure inith node oflth period ofkth year of

jth planning horizon by Wijkl where

i2 Cjk[ Djk[Tj[ Hj.

We also denote the mass flow rate in hth pipe between

nodesiand i0 atlth period ofkth year ofjth short horizonby Vhii0jkl where

h 1; 2;. . .;Wii0j; i; i0 or i0; i 2Pj,

whereWii0jis the number of pipes between nodes iandi0 atjth

short horizon. If the flow of gas in the pipes betweeniandi0 at

lth period ofkth year of jth short horizon is from node ito

nodei0, Vhii0jklis positive; otherwise, it takes a negative value

to indicate that the gas flow direction is from nodei0 to nodei.

2.5.2. Objective function of submodel

The objective function of submodel is the operating costs

of the network. It includes the operating cost of all periodswithin a year:

bjkXtl1

$jkl,

where $jkl is the operating cost paid at lth period of kth

year of jth short horizon. Since we model each period

independently, the annual least operating cost is the sum of

least periodic operating costs:

bjkXtl1

$

jkl,

where$

jkl is the optimum (least) operating cost paid at lthperiod ofkth year ofjth short horizon.

As discussed in Section 2.4.2.2, we consider only the

operating costs of compressor stations and gas supply to

the network. If we denote the total operating costs of gas

supply and compressor stations atlth period ofkth year of

jth short horizon by $cjkl and $s

jkl, respectively, we have

$jkl $c

jkl $s

jkl.

The price of natural gas for each supplier could be a

function of mass flow rate and pressure required. These

price functions should be known in order to run the model.

Let us denote the price function of one mass unit natural

gas inith supply node at lth period ofkth year ofjth short

horizon if requested mass flow rate out of the node and

pressure are M and P, respectively, by psijklM; P. There-fore, the total operating cost of gas supply is

$s

jklX

i2Cjk

Xi02Yi

XWii0jh1

Vhii0jkl

0

@

1

Atl tl1

0

@ psijkl

Xi02Yi

XWii0jh1

Vhii0jkl; Wijkl

0@

1A

0@

1A1A,

Yi fi0ji; i0ori0; i 2Pjg.

We assume that the compressor stations use the natural

gas as energy. The operating cost of a compressor station is

classified into some fixed costs and variable costs. Let us

denote Annual fixed operating cost of a compressor station

of typeTat kth year ofjth short horizon bypfjkTand the

price of one mass unit natural gas consumed in a

compressor station at lth period of kth year of jth shorthorizon by pcjkl. Now, the operating cost of compressor

stations could be defined as

$c

jklX

i;i02Kj

fpfjkmii0jtl tl1

pcjklX

i002Y1i

XWii0jh1

Vhi00ijklX

i0002Y2i0

XWii0jh1

Vhi0i000jklg,

Y1i fi00 i; i00or i00; i 2Pj g,

Y2i0 fi000 i0; i000or i000; i0 2Pj

g.

2.5.3. Constraints of submodel

There are many classes of constraints which limit the

values of the two decision variable sets defined for

submodel. This section mathematically discusses about

these constraints.

Class 1 (Domain of variables):

WijklX0 & real

i2 Cjk[ Djk[ Tj[ Hj

Vhii0jklis real

i; i0 or i0; i 2Pj; h 1; 2;. . .;Wii0j.

Class2 (Pressure limits in demand and supply nodes):gijklpWijklpZijkl

i2 Cjk[ Djk.

Class3 (Gas flow direction in the pipes):

IfWijkl4Wi0jkl3Vhii0jkl40 for h 1; 2;. . .;Wii0j

otherwise ifWijkloWi0jkl3Vhii0jklo0 for h 1; 2; :::; Wii0j

i; i0or i0; i 2Kj

and also

Vhii0jkl Vhi0ijkl

i; i0

or i0

; i 2Pj; h 1; 2;. . .;Wii0j.

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Class4 (Entrance and exit nodes of compressor stations):

IfWijkloWi0jkl3i2 Ij and i0 2Oj,

otherwise ifWijklXWi0jkl3i2 Oj and i0 2Ij,

i; i0ori0; i 2Kj.

Class5 (Mass conservation in nodes):

Demand nodes

Xi02Yi

XWii0jh1

Vhi0ijklyijkl; i2 Djk,

Yi fi0ji; i0 or i0; i 2Pjg.

Supply nodes

ijkpX

i02Yi

XWii0jh1

Vhii0jklpdijk; i2 Cjk,

Yi fi0ji; i0 or i0; i 2Pjg.

Transshipment nodes

Xi2Yi

XWii0jh1

Vhii0jkl0; i2 Aj

Yi fi0ji; i0or i0; i 2Pjg

Entrance and Exit nodes of compressor stations.We assume that the natural gas consumption rate of a

compressor station is a function of the incoming mass

flow rate, pressure at entrance node and pressure at the

outgoing node and the type of station. This function

must be defined by the user of the model. Let us denote

by kM; I; O; T the mass flow rate function consumedby a compressor station of type Twhere the incoming

mass flow rate ofMwith pressure Iis delivered with an

outgoing pressure ofO. Then,

kX

i002Y1i

XWii0jh1

Vhi00ijkl; Wijkl; Wi0jkl; mii0j

0@

1A

X

i002Y1i

XWii0j

h1 Vhi

00ijkl

Xi0002Y2i

0

XWii0j

h1 Vhi

0i000

jkl,

Y1i fi00ji; i00 or i00; i 2Pjg,

Y2i0 fi000ji0; i000 or i000; i0 2Pjg,

i; i0 2Kj; i2 Ij

and also

kX

i0002Y2i0

XWii0jh1

Vhi000i0jkl; Wi0jkl; Wijkl; mii0j

0@

1A

Xi002Y1i

XWii0j

h1

Vhi00ijkl Xi0002Y2i0

XWii0j

h1

Vhi0i000jkl,

Y1i fi00ji; i00 or i00; i 2Pjg,

Y2i0 fi000ji0; i000 or i000; i0 2Pjg,

i; i0 2Kj; i0 2Ij

Class6. Pressure drop

jW2ijkl W2i0jklj zhii0 V2hii0jkl,

i; i0 2Pj; h 1; 2;. . .;Wii0j,

wherezhii0 is the pipe resistant ofhth pipe between nodes i

and i0.

Class 7. Operational constraints of compressor stations.

Compressor stations cannot increase any pressure to any

pressure. These components may not be able to work with

any incoming mass flow rate. Let us denote the set of

feasible vectors of (incoming mass flow rate, inlet pressure,

and outlet pressure) for a compressor station of type Tby

OT. Then,

Xi002Yi

XWii0jh1

Vhi00ijkl; Wijkl; Wi0jkl

0@

1A 2Omii0j,

Yi fi00ji; i00 or i00; i 2Pjg,

i; i0 2Kj; i2 Ij

or equivalently,

Xi002Yi0

XWii0jh1

Vhi00i0jkl; Wi0jkl; Wijkl

0

@

1

A2Omii0j,

Yi0 fi00ji0; i00 or i00; i0 2Pjg,

i; i0 2Kj; i0 2Ij.

3. Optimization algorithm

3.1. Limitations of choosing a solver

Although there are various optimization algorithms

available in the literature of operations research, many of

them are inapplicable to our model because the index range

of decision variables of the integrated model has inter-

dependencies. To clarify these interdependencies, let us

revisit the definition of the decision variables of the

integrated model. We denoted these variables by

(1)Xii0jn2 f0; 1; 2;. . .;rg;

ioi0; i; i0 2Cj;u[Dj;u[Tj[ Hj1;

i; i0eKj1; j 1; 2;. . .;l; n 1; 2;. . .;x,

(2)Yii0j2 f0; 1; 2;. . .;sg;

ioi0; i; i0 2Pj1[Kj1; j 1; 2;. . .;l.

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For j 2; 3;. . .;l, the sets Cj;u;Dj;u; Hj1; P

j1; Kj1 areknown only if the values of decision variables for all previous

short horizons are known; hence, since the index range of the

decision variables of current short horizon depends on these

sets, it means that the index range of decision variables ofjth

short horizon depends on the values of the decision variables

of all previous short horizons.Also, another type of interdependency between the

decision variables exits. The set Pj1 depend on the values

of Xii0jn (see Eq. (1)) as well as the values of decision

variables of all previous short horizons which means the

values of decision variableXii0jnmust be known in order to

know the index range of the decision variable Yii0j.

These interdependencies and the fact that the constraints

and objective function of the model are highly nonlinear

rule out the application of powerful mathematical pro-

gramming approaches and direct use of the metaheuristic

methods available in the optimization literature.

The key point here is that the optimization algorithm for

the model; is not as important as using a robust and

complete model because when a model plans the develop-

ment of the network over a long horizon like 20 years, it

does not really matter for the top managers and policy

makers if the model optimization run time is 1 minute or 10

days! Most of the effort in the literature has diverted to

finding fast solutions to the problem. Considering this fact

and the limitations in choosing an optimization method

due to interdependencies of the index range of the decision

variables, we propose a heuristic random search method in

the next section which sequentially and randomly assigns

values to decision variables and evaluates the objective

function in search of the optimum development plans.

3.2. Steps of the algorithm

We define a complete solution as a feasible combination of

development plans which satisfies all constraints of the

integrated model. In other words, a complete solution

consists of the values of all decision variables for all short

horizons. Also, a feasible development plan for a specific

short horizon is simply called a solution. Therefore, a

complete solution is a combination of solutions of all short

horizons.

The optimization algorithm of the model has an iterative

procedure which produces a number of complete solutions

in each iteration and evaluates their objective functions.

This iterative algorithm continues until one or more of the

terminating conditions of the algorithm are satisfied. The

best found complete solution at the end of the algorithm

converges to global optimum if the number of iterations

goes to infinity. As examples of the terminating conditions,

one may use maximum number of iterations, maximum

number of stalled iterations (consecutive iterations without

any improvement in the objective function of the best

found complete solution), etc.

The algorithm constructs a solution tree in each

iteration which is a set of complete solutions. This tree is

formed as follows. First a feasible solution is created for

the first short horizon (this solution is called the trunk of

the tree or the first level branch; we explain later how a

feasible solution may be created). Knowing the values of

the decision variables of the first short horizon (trunk

solution in the tree), the algorithm creates b2 different

solutions for the second short horizon (these solutions arecalled second-level branches). The trunk solution plus

any one of the second-level branches determine develop-

ment plans of the first and second short horizons. In the

next step, the algorithm creates b3 solutions for the third

short horizon given the trunk solution plus each one of the

second level branches. In a general step j, the algorithm

creates bjsolution for short horizon jgiven any path from

the trunk of the tree to the end of any of the (j1) th-level

branches. Using this procedure, a solution tree would haveQlj2bjcomplete solution where a complete solution is any

path in the graph of the tree from the first-level branch

(trunk) to any one of the lth-level branch. Here, bj :

j 2,3y,l is a user-defined parameter.

A feasible solution for a short horizon is created with a

random search method. The algorithm first assigns values

from set f0; 1; 2;. . .;rg to Xii0jn at random (with a limitedmaximum number of parallel pipes) and knowing the

assigned values of Xii0jn, the algorithm, then, randomly

assigns values from setf0; 1; 2;. . .;sg to Yii0j. Knowing thevalues of both decision variables, the constraints of the

integrated model are checked to determine the feasibility of

the solution comprised of the values of both decision

variables. If all constraints are satisfied, a feasible solution

has been produced. Verification of constraints of integrated

model requires running the control optimization submodelfor each period of each year of the corresponding short

horizon. We use a genetic algorithm approach for finding

(near) optimal solution of the submodel.

When a tree is constructed in an iteration, the objective

function of each complete solution in the tree is evaluated

using the objective function of the integrated model which

consists of capital cost of the new physical components of

the network to be installed in development plans plus the

optimum operating cost of utilizing the network during the

long-run horizon obtained by running the submodel. The

best combination of development plans after a number of

iterations of the optimization algorithm would be the

created complete feasible solution with least objective

function.

4. Case study

This section demonstrates the application of the model

and designed heuristic optimization algorithm to a

simplified case study.

4.1. Definitions and parameters

An arbitrary study area requires a strategic plan for

development of an existing natural gas transmission

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pipeline network in order to satisfy the demand of a

number of major consumers from January 1, 2010 to

December 31, 2020 (o 10). This 10-year long-run

horizon is split into two 5-year short horizons (l 2,

u 5) and the goal is to find 2 development plans with least

discounted operating and capital costs. We assume there is

ample time before 2010 to implement the first developmentplan.Table 3summarizes some parameters of the model of

this case study. Fig. 1 shows the existing network before

the development plans are implemented and Table 4

provides the location of the nodes in Fig. 1. Tables 5 and

6show the type of pipelines and compressor stations in the

available network, respectively.

We consider a 25 km square grid in the map for the

location of the transshipment nodes for both development

plans. Also, another assumption is that no new demand or

supply node would be added during the long-run horizon.

Table 7 shows the forecasted consumption rate of the

demand nodes in each short-run horizon (for simplicity, we

assumed one period in each year and similar consumption

rate in each year).Table 8shows the range of production at

supply nodes over the long-run horizon. The supply nodes

can provide natural gas with a pressure between 700 and

1050 psi. The demand nodes require a gas pressure with the

same range. Also, the pressure of gas entered to a

compressor station may not fall below 700 psi and the

maximum outlet pressure from a compressor station could

not be more than 1050 psi.

Table 9shows the price of one unit of natural gas over

the long run horizon. For simplicity, we assume the

incoming and outgoing mass flow rates of compressor

stations are equal (this is a bit different from ourassumption in the model that compressor stations consume

a fraction of flowing natural gas). Consequently, we

assume the operating cost (dollar) of a compressor station

for a short horizon is calculated as follows:

operating cost 540; 000VinPout

Pin

0:4=1:4,

where Vin is the daily volumetric incoming flow rate, Pinthe inlet pressure and Pout the outlet pressure.

We also calculate the capital cost (dollar) of a

compressor station throughout the long horizon using the

following formula:

operating cost 485 877Vin.

Table 10shows the capital cost of installing 100 km of

pipelines in the study area throughout the long horizon (we

assume installation location doesnt affect the cost).

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Table 3

Parameters of the model

Parameter Value

o 10

u 5

l 2

t 1

r 14

s 1

x 2

w 0%

S

S

S

D D

DT

T

C C

C

C

D

5

6

11

4

1

7 9

12

2

8 13

3 10

Legend:S: supply nodeD: demand nodeC: compressor station end nodeT: active transshipment nodes

Fig. 1. The graph of the available network before implementation of the

first development plan.

Table 4

Location of the nodes of the available network before implementation of

the first development plan

Node Location (km, km)

1 (25,0)

2 (25,100)

3 (25,100)

4 (50,100)

5 (0,150)

6 (50,175)

7 (50,150)

8 (75,150)9 (75,150)

10 (75,100)

11 (125,150)

12 (125,100)

13 (175,150)

Table 5

Types of pipeline edges of the available network

Edge Type

(1,2) 8

(3,4) 8

(5,7) 10(6,7) 9

(4,7) 8

(7,8) 8

(8,10) 8

(9,11) 8

(4,10) 8



12/15

4.2. Results

We used 1000 iterations of the optimization algorithm

with b23; which means that the algorithm has created3000 complete solutions. The optimum complete solution

found in the first 1000 iterations had very simple

development plans which suggest these solutions:

Optimum solution of the first short horizon (require-ments of development plan 1):J Install a pipeline of type 7 between nodes 11 and 13

(X11;13;1;1 7).J Install a pipeline of type 7 between nodes 11 and 12

(X11;12;1;1 7).

Optimum solution of the second short horizon (require-ments of development plan 2):J Do not change the network.

Fig. 2 shows the network after implementing the first

development plan (since the network does not change in

development plan 2, the figure represents the availablenetwork during short horizon 2 as well).

The total operating cost during the long horizon for the

optimal complete solution was $14,020,969 and the capital

cost was $14,000,000. Since we set the discount rate equal

to zero, the NPW (objective function) of the optimal

complete solution is simply the sum of the operating and

capital cost, $28,020,969.

One of the possible reasons that the optimization

algorithm recommended no change to be made in

development plan 2 is that the discount rate was zero,

which means paying capital cast late and saving cash at the

beginning of the long horizon has no advantage.

5. Discussion

Development of natural gas transmission networks

could affect different sectors such as economy, society,

environment, and politics. So far, we discussed about the

most evident issues in network development planning

including technical, structural and economics of the pipe-

line network. In this section, we discuss how other issues

such as environmental, social, safety, and political criteria

could be incorporated into a typical network development

project in general and our model in particular.Some parts of these issues are beyond the scope of the

model of this paper. The proposed model covers only the

first phase of a typical network development project as

outlined in Table 2 and for instance, many of the

environmental concerns could be considered in the last

phases of a network development project (installation and

inspection) and are unrelated to our strategic planning

model.

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Table 6

Types compressor station edges of the available network

Edge Type

(8,9) 1

(2,3) 1

Table 7

Forecasted consumption rates of the demand nodes

Demand

node

Consumption rate throughout

the first short horizon

(million m3)

Consumption rate throughout

the second short horizon

(million m3)

4 7 11

6 20 22

11 12 13

12 9 18

Table 8

Range of production rates of the supply nodes

Supply node Supply rate throughout the

first short horizon

(million m3)

Supply rate throughout the

second short horizon

(million m3)

Min Max Min Max

1 5 10 10 15

5 25 40 35 50

13 0 30 0 40

Table 9

Price of natural gas

Supply

node

Forecasted price throughout

the first short horizon ($/

million m3)

Forecasted price throughout the

second short horizon ($/

million m3)

1 30 33

5 36 42

13 45 49Table 10

Capital cost of installing 100 km pipeline

Pipeline type Installation cost (million$)

1 4

2 6

3 8

4 10

5 12

6 16

7 20

8 24

9 30

10 36

11 40

12 42

13 48

14 56



13/15

Another key point is that some of the criteria whose

effects are important on network development planning are

satisfied when the network itself develops even if these

criteria are not directly considered in the model

(for example, see Sections 5.1). In multiobjective optimiza-

tion language, such criteria are not in conflict with the

objective function of the model and one need not worry

about them.

Multiobjective optimization methods are useful only for

conflicting criteria of network development planning. There

are many types of multiobjective functions; two well-knowntypes of them are (1) minfmaxx2Ff1x;f2x;. . .;fkxg(orsimilarly max min) and (2) minx2Ff1x;f2x;. . .;fkx;wherex is the decision vector, Fthe set of feasible decision

vectors, and fi is the ith objective function. For the first

type, one may add some constraints to the problem and

reduce the objective function to a single-objective function

(see Hillier and Liberman, 1997). The most widely used

technique for the second type consists of reducing the

multiobjective problem to a single objective one by means

of the so-called scalarization procedure. Various scalar-

ization procedures may be employed:

1. Cost function method: Each objective function is

assigned a cost coefficient and then the function

obtained by summing up all the objective functions

scaled by their cost coefficients is optimized.

2. Goal programming method: An ideal optimal value for

each objective function is chosen and then the Eu-

clidean/absolute distance between the actual vector of

objective functions and the vector made up of the ideal

values is optimized.

The optimization algorithm described in Section 3 is

basically a numerical optimization method, i.e. it only

needs numerical values of objective function and does not

use the form of the objective function. Hence, this property

along with the fact that the constraints of the model are not

changed with different objective functions enable the model

to have multiobjective functions if any of the above

multiobjective techniques are employed to transform the

multiobjective function to a single one.

In addition to the ability of the model to accept acompletely new multiobjective function, we also believe

that current cost-based single-objective function of the

model has the potential to account for some other

conflicting criteria if an appropriate cost function method

briefly explained above is employed. For instance, one may

measure environmental or safety criteria with money

and add these cost to the cash flow of the current NPW

objective function or select appropriate locations for

transshipment nodes (we elaborate upon this approach in

the subsequent sections).

5.1. Environmental concerns

Sustainable development requires protection of natural

environment; and expansion of a natural gas transmission

network could have significant impacts on environment.

Some environmental criteria of network planning have

clear conflicts with the economy of expansion in certain

geographical areas, but some others do not.

Natural gas is a green fossil fuel which pollutes the

environment less than the others. Because of its clean

burning nature, the use of natural gas wherever possible,

either in conjunction with other fossil fuels or instead of

them can help reduce the emission of harmful pollutants.

In this view, development of the network in our model evenwith its microeconomic goals improves environmental

indicators.

On the other hand, preservation of trees and natural

habitats is a concern that sometimes conflicts with

economic objectives of the network development plans

because an economically optimum plan may require

cutting trees or trespassing protected habitats. The planner

in this situation may be presented with two options:

1. Pay the cost of violating the environment (cutting trees,

trespassing habitats, or any harmful interference in

ecosystem): this cost may be paid to certain institutions

(for example to obtain the right of way) or spent for

compensating the impacts on environment by turning

the environmental situation after implementing the plan

to the position before that.

2. Money cannot do anything. Violation of the environ-

ment in the area is absolutely prohibited.

The capital cost of installing a pipeline in the objective

function of the integrated model was a function of the

location of the installation. For the first option above

which let the planner pay the cost of installing pipes in an

environmentally protected area, this cost could easily be

considered in the capital cost of the pipeline passing the

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S

S

S

D D

DT

T

C C

C

C

D

5

6

11

4

1

7 9

12

2

8 13

3 10

Legend:S: supply nodeD: demand nodeC: compressor station end nodeT: active transshipment nodes

Fig. 2. The graph of the network after implementing optimal development

plan 1.



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protected area; and for the second option, no transship-

ment node is considered inside the protected area and an

infinite cost of installation is assumed in the model which

recommends the optimization algorithm not to trespass the

absolutely protected area or pay an infinite cost.

5.2. Social issues

Social justice is based on the idea of a society which

gives individuals and groups fair treatment and a just

share of the benefits of society. Governments seek to

provide a minimum level of income, service, or other

support for disadvantaged peoples to improve indicators of

social justice and welfare. Natural gas is one of these

services that could be used as a tool to pursue certain social

policies.

A common problem in developing countries is centrali-

zation of the country resources, income and welfare in

limited metropolitan areas (such as Tehran, Khomei-

nishahr, Shahinshahr and Varnosfaderan State in Iran).

This geographically unbalanced development causes many

social and economical problems for people living far from

these developed areas. These problems include migration to

metropolitan areas, unemployment, and in general, poor

standards of living and quality of life outside major cities.

In the perspective of natural gas development planning, the

governments may indirectly subsidize the physical devel-

opment of the network in certain geographical areas to

supply cheaper gas to rural and undeveloped areas and

share the benefits of using this source of energy more fairly

and improve social justice. These subsidies could be

subtracted from the capital cost of installing pipelinesand compressor stations for undeveloped areas in our

model.

5.3. Reliability and safety

The integrity of the pipeline network and its related

equipment is one of the industrys top concerns. The threat

of catastrophic pipeline rupture, though extremely unlikely

given the industrys safety precautions, hangs over the

head of every pipeline executive and employee. Pipe-

lines require regular patrol, inspection, and maintenance

including internal cleaning and checking for signs of gas

leaks.

Poor reliability and safety measures in a network could

result in various failures and damages. Corrosion is a

serious problem plaguing the industry. This is a sneaky

enemy and unless it has caused obvious damages, corrosion

is very difficult to detect and locate accurately. To

minimize corrosion, pipeline companies install electrical

devices called catholic protection systems, which inhibit

electrochemical reactions between the pipe and the

surrounding materials. Mechanical damages also occur

when heavy construction equipments dent the pipe, scrape

off its coatings, gouge the metal or otherwise deform the

pipe in some way. However, if the pipeline has to be shut

down for any reason, the production and receiving facilities

and refineries often also have to be shut down because gas

cannot be readily stored, except perhaps by increasing the

pipeline pressure by some percentage. All these damages

and failures involve cost.

Reliability and safety criteria could be incorporated into

the cost-based objective function of the model if themodeler could measure the level of reliability in cost. The

reliability cost has two parts. The first part is a fixed cost

which is paid at the time of installing a physical component

of the network. This cost should be considered in the

capital cost of the component (pipeline or compressor

station). The second part is the cost of inspections and

safety measures after the physical components of the

network are installed. Obviously, this part of the reliability

cost is a part of the operating cost.

The development plans in the model are based on the

forecasts of the consumption in demand nodes and

production range in supply nodes. But, the actual

production or consumption during the long horizon may

deviate from forecasts. The network must be reliable in this

situation to provide actual demanded natural gas of the

consumers during the long-run horizon. The risk of poor

reliability in this case is significant because inadequacy of

supplied natural gas to certain consumers like large

manufacturing industries or power plants could shut down

these facilities for a longer period of time than a failure in

the network. Also, when inadequate natural gas is

supplied, consumers may use more polluting fuels and this

problem leads to environmental damages. However, this

problem could be addressed in the model by applying a

margin of safety to the forecasts or accounting for the costof probable inadequate supply of natural gas in the

objective function.

5.4. Politics

Regional economic collaborations possess the power to

engender as well as transform social and political discourse

between countries. Energy ties play a more important role

in the economics and politics of energy rich countries. Such

regional and international energy relations sometimes serve

the political goals of the countries. For instance, since the

discovery of natural gas reserves in Irans South Pars fields

in Persian Gulf in 1988, the Iranian government began

increasing efforts to promote higher gas exports abroad.

The export of this energy resource could end political

isolation of the country. With this aim, Iran is negotiating

with India and China to export natural gas to these

large regional consumers in the near future. In our

model, each natural gas export terminal in the long-run

horizon is a demand node; therefore, the export quantities

at these nodes should be forecasted. The governments

may subsidize installing physical components of net-

work structure and reduce associated capital costs to

encourage the export. Such policies could help political

interests.

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6. Conclusion

In this paper, we developed a new model for finding the

optimal development plans over a long horizon. This

nonlinear model accounts for various engineering and

economic factors related to the problem. The objective

function is essentially the NPW of all related operating andinvestment costs paid during the long-run study horizon.

We study the feasibility of the development plans through

different constraints. In addition to the planning model, a

heuristic random search optimization algorithm was

developed which finds (near) optimal solutions of the

model. A case study was used to demonstrate the

application of the model and optimization algorithm.

Although our model was originally designed to meet the

planning difficulties in Iran with a noncompetitive gas

market and monopoly decision-making environment, but

we believe it could be applied to other cases as well. The

major step in implementing the model is collecting the

necessary information to feed into model. Accuracy of the

data and forecast could improve the optimality of

development plans suggested by running the model. We

are working on implementing the model on Irans network.

We also intend to extend the applicability of the model by

releasing some assumptions and introducing new cost

elements in the objective function.

Acknowledgment

This work was supported in part by National Iranian

Gas Company. The authors would like to thank Ms.

Khaleye M. Hemmati for her considerate cooperation withus during this research.

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